If `intsqrt(1+sinx)f(x)dx=2/3(1+sinx)^(3/2)+c ,t h e nf(x)e q u a l` `cosx` (b) `sinx` (c) `tanx` (d) 1

int(e^(-x/2)sqrt(1-sinx))/(1+cosx)dx

int(e^(-x/2)sqrt(1-sinx))/(1+cosx)dx

If int (e^(x)(1+sinx))/(1+cosx) dx = e^(x) f(x) + c then f(x) =

int e^(-(x)/(2)) (sqrt(1 -sinx))/(1 + cosx ) dx =

("lim")_(xto0)((1+tanx)/(1+sinx))^(cos e cx)i se q u a l t o (a)e (b) 1/e (c) 1 (d) none of these

If intsin^(-1)xcos^(-1)xdx=f^(-1)(x)[π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+C ,t h e n (a) f(x)=sinx (b) f(x)=cosx (c) f(x)=tanx (d) none of these

int(sinx-cosx)/(sqrt(1-sin2x))e^(sinx)cosx dx is equal to

int(sinx-cosx)/(sqrt(1-sin2x))e^(sinx)cosx dx is equal to

If y=(sinx)^(tanx),t h e n(dy)/(dx)= (a) (sinx)^(tanx)(1+sec^2xlogsinx) (b) tanx(sinx)^(tanx-1)cosx (c) (sinx)^(tanx) (d) sec^2xlogsinx tanx(sinx)^(tanx-1)